Всероссийский научно-исследовательский институт метрологии (ВНИИМ)
им. Д. И. Менделеева (Санкт-Петербург)

Отдел 202: Теоретической и квантовой метрологии
Сектор 2021: Прецизионной физики и метрологии простых атомных систем

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Физика простых атомов и ее приложения
(Путеводитель по простым атомам)
- Простые атомные системы
- Уровни энергии в простых атомах
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- Оптические переходы в водороде
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Приглашенные доклады
  • С. Г. Каршенбойм.  Лэмбовский сдвиг в атоме водорода. XV Конференция: Фундаментальная атомная спектроскопия. Звенигород. 1996.
  • S. G. Karshenboim. The hydrogen Lamb shift and the proton radius. In Proceedings of the International Workshop Hadronic Atoms and Positronium in the Stardard Model (Dubna, 1998). Ed. By M. A. Ivanov et al., Dubna (1998) 224-231. Электронный препринт: hep-ph/0008137
  • S. G. Karshenboim. The proton radius as measured by optical methods. In Proceedings of the 15th Students' Worsshop on Electromagnetic Interactions. Bosen (1998) pp.87-101.
  • S. G. Karshenboim. Hydrogenic Bound States. Invited talk at International Symposium  Lepton Moments. Heidelberg, 1999. Прозрачки.
  • S. G. Karshenboim. Precise Physics of Simple Atoms. Atomic Physics 17 (AIP conference proceedings 551) Ed. by E. Arimondo et al. AIP, 2001, pp. 238-253. Электронный препринт: hep-ph/0007278. Invited talk at International conference on Atomis Physics 2000 (Florence). Abstract.
  • S. G. Karshenboim. Laser spectroscopy of simple atoms and precision tests of bound state QED. Invited talk at 3rd Simposium on Modern Problems of Laser Physics. Novosibirsk, 2000. Электронный препринт: physics/0008215. Abstract.
  • S. G. Karshenboim. g factor of a bound electron in hydrogen-like ions. An invited talk at ITAMP Workshop Wave Functions and QED Effects in Few-Electron Atoms. Harvard, 2000. Прозрачки.
  • S. G. Karshenboim. Possible laboratory search for variation of fundamental constants. An invited talk at 250. WE-Heraeus Seminar Presision Experemints and Fundamental Constants in Physics, Bad Honnef 2001. Abstract.
  • S. Karshenboim. Precision Study of Positronium, Presented at 9th International Workshop on Slow Positron Beam Techniques for Solids and Surfaces (SLOPOS), Dresden, 2001. Abstract.

  • S. G. Karshenboim, Simple atoms, Quantum electrodynamics and fundamental constants. PSAS'2002 (St. Petersburg, 2002).
  • S. G. Karshenboim, Laboratory search for variation of fundamental constants. Australian Institute of Physics: 15th Biennial Congress (Sydney, 2002).
  • S. G. Karshenboim, Simple atoms: QED tests and fundamental constants. Australian Institute of Physics: 15th Biennial Congress (Sydney, 2002).
  • S. G. Karshenboim, Time and physical constants. International Colloquium on Time and Matter (Venice, 2002).
  • S. G. Karshenboim, QED theory of hydrogen-like atoms. Third Workshop on Hadronic Atoms (CERN, 2002).
  • S. G. Karshenboim, Variation of the Fine-Structure Constant. HYPER SYMPOSIUM (Paris, 2002).
  • S. Karshenboim, Precision study of positronium and precision tests of the bound state QED. (Workshop on Positronium Physics, ETH Zurich, 2003).
  • S. G. Karshenboim, Precision tests of QED and the fine-structure constant, an invited talk at International Workshop on Fundamental Interactions (ECT* European Centre for Theoretical Studies in Nuclear Physics and Related Areas, Trento, 2004).
  • S. G. Karshenboim, P. Fendel, V. G. Ivanov, N. Kolachevsky and T. W. Haensch, 2s Hyperfine Structure in Hydrogen and Deuterium: a Precision Test of QED, an invited talk at Hydrogen atom 3: Precision Physics of Simple Atomic Systems (Mangaratiba, 2004).
  • S. G. Karshenboim, Laboratory searches for a time variation of fundamental constants, an invited talk at 9th Summer Institute at Gran Sasso National Laboratory on Particles, Gravity and Cosmology, 2004.

Тезисы приглашенного доклада на международную конференцию ICAP 2000
Precise Physics of Simple Atoms

Savely G. Karshenboim

D. I. Mendeleev Institute for Metrology, St. Petersburg, Russia
Max-Planck-Institut fuer Quantenoptik, Garching, Germany

Simplicity of “simple” atoms has been for a while a challenge to precision theory and experiment. Are the simple hydrogen-like atomic systems simple enough to be calculated with an accuracy, appropriate to compete to the best experimental results? That is a question, that theorists have tried to response. The most simple atoms are different two-body bound systems with a low value of the nuclear charge: Z = 1 (hydrogen, deuterium, muonium and positronium) and Z = 2 (single-charged ions of helium-3 and helium-4) etc. We present state of art in physics of simple atoms and discuss in detail theoretical and experimental status of studying such atoms.

In particular, we consider few theoretical problems:

  • Small parameters for simple atoms are lower than 1/100 (= 1/137, =1/207 etc), however, most of known expansions over them used to behave not quite well because of large logarithms (ln(1/) ~  ~ 5) and large numerical coefficients. Appearance of increasing powers of these large logarithms make any estimation of a theoretical accuracy to be a hard problem.
  • Two kinds of higher-order QED corrections have not been known up-to-date and limit the precision of the present theoretical evaluations. One of them arises from expansions of the electron two-loop self-energy contribution in strengh of the Coulomb interaction (). That is a problem to compute the Lamb shift in the hydrogen, helium ion and some higher-Z atomic systems. Similar higher-order (in ()) terms should appear for calculations of a bound electron g-factor in hydrogen-like ions at Z~20-30.
  • The other important task is to evaluate radiative-recoil contributions with essential binding effects. Such contributions are important for the hyperfine structure in muonium and for positronium spectrum.
  • Important problem is contributions beyond QED and, in particular, influence of strong interactions. For instance, our possibility to do any calculation for the hydrogen and deuterium atoms is completely limited now by our knowledge of the proton and deutron structure.
Most of these questions and a more broad range of problems in physics of simple atoms were considered at a Satellite meeting to the ICAP (Hydrogen Atom, 2: Precise Physics of Simple Atomic System) and in their book of abstracts one can find detail on theoretical and experimental status of physics of simple atoms, including hydrogen, muonium, positronium, helium, few-electron ions at different Z, muonic and exotic atoms, antihydrogen. Several metrological problems due to precison spectroscopy and determination and possible variation of fundamental constants were also among the topics of the satellite meeting.

Тезисы приглашенного доклада на международную конференцию MPLP’2000
Precision spectroscopy of simple atoms and tests of the bound state QED

Savely G. Karshenboim

D. I. Mendeleev Institute for Metrology, St. Petersburg, Russia
Max-Planck-Institut fuer Quantenoptik, Garching, Germany

Precision laser spectroscopy of simple atoms (hydrogen, deuterium, muonium, positronium etc) provides an opportunity to precisely test Quantum Electrodynamics (QED) for bound states and to determine different fundamental constants with a high accuracy. The talk is devoted to a comparison of theory and experiment for the bound state QED.

The QED for free particles (electrons and muons) is a well-established theory designed to perform different calculations of particle properties (like e. g. anomalous magnetic moment) and of scattering cross sections. In contrast, the theory of the bound states is not so well developed and it needs further precision tests.

Experimental progress during the last ten years has been mainly due to laser spectroscopy and, thus, the bound state QED tests are an important problem associated with modern laser physics.

The QED theory of the bound states contains three small parameters, which play a key role: the QED constant , the strength of the Coulomb interaction  and the mass ratio m/Mof an orbiting particle (mainly – electron) and the nucleus. It is not possible to do any exact calculation and one needs to use some expansions over some of these three parameters.

The crucial theoretical problems are:

  • The development of an effective approach to calculate higher-order corrections to the energy levels.
  • Findig an effective approach to estimate higher-order corrections to the energy levels.
The difference between these two problems is very important: any particular evaluations can include only a part of terms and we must learn how to determine the uncertainty of the theoretical calculation, i. e. how to estimate corrections that cannot be calculated.
We consider higher order QED corrections, our knowledge on which determines the accuracy of the bound state QED calculations. We particularly discuss: the Lamb shift in hydrogen and light hydrogen-like atoms, hyperfine structure in muonium and positronium, 1s-2s and fine structure of positronium etc.
After recent calculations of the one-loop, two-loop and three-loop corrections to the Lamb shift in the hydrogen atom the main uncertainty comes from higher order two-loop contributions of the order . They contain a large logarithm  and the leading term with the cube of the logarithm is known [1]. The uncertainty due to the uncalculated double logarithms is estimated as 2 ppm.
A specific combination of the Lamb shifts

is important [2] for the evaluation of data of optical measurements from Garching and Paris, obtained by means of two-photon Doppler-free laser spectroscopy. The uncertainty in this difference is also determined by unknown terms, but the leading terms which includes a squared logarithm is known [2].

The hyperfine structure of the ground state in the muonium atom is a precisely measured value. The uncertainty of the calculation is due to unknown corrections of the fourth order. Some of these, including the large logarithms ( or ), are known [3] and non-leading terms limit the uncertainty of the theoretical expression as 0.05 ppm. The uncertainty arises from the unknown next-to-leading radiative-recoil () and pure recoil () terms. The largest uncertainty comes from a calculation of the leading term because of the lack of a precise knowledge of the muon-to-electron mass ratio. One way to determine this ratio is the 1s-2s muonium experiment.

For the case of the positronium spectrum there are a number of value which were or are under precision experimental study. In all cases the uncertainty of the positronium energy (n = 1, 2) is known up to . The only double logarithm is known to the next order. The inaccuracy originates from the non-leading terms (single logarithm and constant) of radiative and radiative-recoil corrections of order .
In our talk we discuss briefly also some other values. The brief review shows that now the crucial corrections in the bound state QED are:
  • higher order two-loop corrections;
  • radiative-recoil and pure recoil terms of order , the calculation of which involves an essential part of the QED, binding and two-body effects .
Most problems concerning the study of simple atoms were discussed at the recent Hydrogen atom, 2 meeting, which took place this June in Italy and one can find more references on the subject therein [4].
  1. S. G. Karshenboim, JETP 76 (1993) 541.
  2. S. G. Karshenboim, Z. Phys. D 39 (1997) 109.
  3. S. G. Karshenboim, Z. Phys. D 36 (1996) 11.
  4. Hydrogen Atom II: Precision Physics of Simple Atomic Systems. Book of abstracts (ed. by S. G. Karshenboim and F. S. Pavone), Castiglione della Pescaia, 2000.

Тезисы приглашенного доклада на международный семинар 250. WE
Possible laboratory search for variation of fundamental constants

Savely G. Karshenboim

D. I. Mendeleev Institute for Metrology, St. Petersburg, Russia
Max-Planck-Institut fuer Quantenoptik, Garching, Germany

A possibility of variation of value of some physical constants was proposed long time ago. Up to now there has been no reasonable common model to describe such a variation. Recent attempts to detect some variations have led to limitations for fractional variation of some constants on level of 10-3-10-5 during the lifetime of our Universe. 

Different options for the search for possible variations are considered in the talk and a short overview of the results obtained with several methods is given. Their advantages and disadvantages are discussed with respect to simultaneous variations of all constants in both time and space in range 108-1010 yr. A few possibilities for the laboratory search are suggested [1]. In particular, we propose some experiments with the hyperfine structure interval in atomic hydrogen, deuterium and ytterbium-171 and in some atoms with small nuclear magnetic moments. Since most of precisely measured frequencies are due to hyperfine structure transitions we pay special attention to interpretation of such measurements in terms of variation of fundamental constants. 


1. S. G. Karshenboim, Can. J. Phys. 78, 639 (2000).

Последняя модификация: 06 декабря 2005 г. (С. Г. Каршенбойм)